Local sequence alignments statistics: deviations from Gumbel statistics in the rare-event tail.
Local sequence alignments statistics: deviations from Gumbel statistics in the rare-event tail.
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DOI：
10.1186/1748-7188-2-9
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发表时间：
2007-07-11
期刊：
影响因子：
--
通讯作者：
Hartmann AK
中科院分区：
文献类型：
--
作者：
Wolfsheimer S;Burghardt B;Hartmann AK
无限长随机序列的无空位局部比对的最优得分已知遵循Gumbel极值分布。对于允许出现间隙的重要情况，人们所知甚少。在这种情况下，仅在高概率区域中凭经验知道分布，这在生物学上不太相关。我们提供了一种方法来获得数值上的分布的生物相关的罕见事件的尾巴。该方法，这已经概述了在早期的工作中，是基于生成的序列与参数化的概率分布，这是有偏见的相对于原始的生物，在大都会耦合马尔可夫链蒙特卡罗的框架。在这里，我们首先详细介绍了该方法，并通过考虑一个简单的测试用例来评估算法的收敛性。在早期的工作中，该方法只适用于一个单一的例子。因此，我们在这里考虑一个大的参数集：我们研究了不同的替代矩阵（BLOSUM62和PAM250）和仿射间隙成本与不同的参数值的蛋白质比对的分布。在对数阶段（大缺口成本），以前假设Gumbel形式仍然成立，因此在评估数据库中的p值时通常使用Gumbel分布。在这里，我们表明，对于所有情况下，只要序列不是太长（L > 400），一个“修改”的Gumbel分布，即一个额外的高斯因子的Gumbel分布是适合描述的数据。我们还提供了一个“缩放分析”的修改后的Gumbel分布中使用的参数。此外，通过与BLAST参数的比较，我们表明，显着性估计的变化相当大时，使用这里提出的真实分布。最后，我们还研究了k个最佳比对的和统计量的分布。我们的研究结果表明，统计的空位和ungapped本地对齐偏离Gumbel在稀有事件的尾巴显着。我们提供了一个高斯校正的分布和分析其缩放行为的几个不同的评分参数集，这是常用的搜索蛋白质数据库。包括k个最佳比对的和统计的情况。
The optimal score for ungapped local alignments of infinitely long random sequences is known to follow a Gumbel extreme value distribution. Less is known about the important case, where gaps are allowed. For this case, the distribution is only known empirically in the high-probability region, which is biologically less relevant. We provide a method to obtain numerically the biologically relevant rare-event tail of the distribution. The method, which has been outlined in an earlier work, is based on generating the sequences with a parametrized probability distribution, which is biased with respect to the original biological one, in the framework of Metropolis Coupled Markov Chain Monte Carlo. Here, we first present the approach in detail and evaluate the convergence of the algorithm by considering a simple test case. In the earlier work, the method was just applied to one single example case. Therefore, we consider here a large set of parameters: We study the distributions for protein alignment with different substitution matrices (BLOSUM62 and PAM250) and affine gap costs with different parameter values. In the logarithmic phase (large gap costs) it was previously assumed that the Gumbel form still holds, hence the Gumbel distribution is usually used when evaluating p-values in databases. Here we show that for all cases, provided that the sequences are not too long (L > 400), a "modified" Gumbel distribution, i.e. a Gumbel distribution with an additional Gaussian factor is suitable to describe the data. We also provide a "scaling analysis" of the parameters used in the modified Gumbel distribution. Furthermore, via a comparison with BLAST parameters, we show that significance estimations change considerably when using the true distributions as presented here. Finally, we study also the distribution of the sum statistics of the k best alignments. Our results show that the statistics of gapped and ungapped local alignments deviates significantly from Gumbel in the rare-event tail. We provide a Gaussian correction to the distribution and an analysis of its scaling behavior for several different scoring parameter sets, which are commonly used to search protein data bases. The case of sum statistics of k best alignments is included.
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DOI：
10.1073/pnas.89.22.10915
发表时间：
1992-11-15
影响因子：
11.1
作者：
HENIKOFF, S;HENIKOFF, JG
通讯作者：
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DOI：
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影响因子：
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